The problem of the decoding of a shaped set is formulated in terms of a zero-one linear program. Some special features of the problem are exploited to relax the zero-one constraint, and to substantially reduce the complexity of the underlying simplex search. The proposed decoding method has applications in fixed-rate entropy-coded vector quantisation of a memoryless source, in decoding of a shaped constellation, and in the bit allocation problem. The first application is considered and numerical results are presented for the quantisation of a memoryless Gaussian source demonstrating substantial (of the order of a few tens to a few hundred thes) reduction in the complexity with respect to the conventional methods based on dynamic programming. It is generally observed that the complexity of the proposed method has a linear increase with respect to the quantiser dimension. The corresponding numerical results show that it is possible to get very close to the bounds determined by the rate-distortion theory, while keeping the complexity at a relatively low level.
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